Problem: Solve for $x$ and $y$ using elimination. ${-5x-2y = -18}$ ${-2x+2y = 4}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-7x = -14$ $\dfrac{-7x}{{-7}} = \dfrac{-14}{{-7}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-5x-2y = -18}\thinspace$ to find $y$ ${-5}{(2)}{ - 2y = -18}$ $-10-2y = -18$ $-10{+10} - 2y = -18{+10}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-2x+2y = 4}\thinspace$ and get the same answer for $y$ : ${-2}{(2)}{ + 2y = 4}$ ${y = 4}$